Free and mixed convection boundary layer flow, heat and mass transfer in nanofluid using buongiorno model

The Buongiorno model is used in the study which takes into account the effects of Brownian motion and thermophoresis on free and mixed convections boundary layer problem. The governing partial differential equations are transformed into a nonlinear ordinary differential equations using similarity transformations. These ordinary differential equations are then solved numerically using shooting method with the help of Maple software and bvp4c codes in Matlab software. Numerical results for the skin friction coefficient, local Nusselt number and local Sherwood number as well as velocity, temperature and nanoparticle concentration profiles are presented graphically. The governing parameters in this study are Brownian motion parameter Nb, thermophoresis parameter Nt, suction parameter S, mixed convection parameter l, stretching or shrinking parameter e, velocity ratio parameter v, velocity slip parameter s, Biot number Bi, nonlinear parameter n, curvature parameter g, Soret number Sr and Dufour number Du. It is observed that the skin friction coefficient and local Nusselt and Sherwood numbers both represent the heat and mass transfer rate are significantly controlled by these parameters. Brownian motion and thermophoresis parameters are able to enhance the heat transfer rate when both have small values. An increment of the heat transfer rate increases the cooling process, while the decrement of heat transfer rate enhanced the heating process at the surface. Dual solutions are found exists for a certain range of suction, stretching or shrinking, mixed convection and moving parameters. It is noticed that suction and partial slip widens the range in which the dual solutions exist. Furthermore, the first solution is found stable meanwhile the second solution is unstable and it is obtained by performing a stability analysis.

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